help with a pre-calculus homework problem?

[Kimberly M]

A statement S(sub n) about the positive integers is given. Write statements S(sub k) and S(sub k+1) simplifying S(sub k+1) completely.

S(sub n): 1*2+ 2*3+ 3*4+... n(n+1)= (n(n+1)(n+2))/3